Dark Matter

Could quantum mechanics be related to dark matter? As in new 'stuff" is being made therefore pushing the time space in between galaxies apart. Which to me makes sense as time and space is created (The Big Bang) wouldnt it be created on the quantum level? Couldnt this still be going on in the universe which gives credit to why the universe is speeding up as it is expanding on the inside also from the outside?

Forgive me for not actually addressing your question, but you're talking about dark energy not dark matter. Dark matter is the source of additional gravity pulling things together (namely galaxies and galaxy-clusters). Dark energy is what causes the universe to accelerate its expansion, dark energy is also referred to as the 'cosmologically constant'.

Essentially, the first thing that popped into people's minds when dark energy was discovered (and before, probably) was that it was a quantum mechanical effect known as vacuum energy. Unfortunately, all predictions were off by a factor of about 10^121, making it without a doubt the worst prediction in the history of physics.

Dark energy is almost certainly somehow related to quantum mechanics, but the exact mechanism is far from trivial.